David Cameron's Davos speech, setting out his agenda for the G8 summit this summer, was a clever attempt to move the debate about how to alleviate world poverty beyond the stale politics of totting up international aid budgets, at a time when rich governments are tightening their belts.

At the G8 summit in the Scottish golf resort of Gleneagles in 2005, Tony Blair basked in the glory of grateful African leaders after a raucous public campaign to "Make Poverty History", and a lot of diplomatic arm-twisting helped him secure a pledge to ramp up aid budgets towards 0.7% of GDP.

Eight years later, as Britain takes on the rotating G8 presidency once again, David Cameron is operating in a less optimistic, more financially constrained and splintered world.

Emerging economies that have watched the west implode in the financial crisis are reluctant to listen to lecturing from the G8; aid budgets are under pressure, with Britain one of the few countries living up to its G8 promises; and the growing importance of the G20 – which also includes the major developing countries – has left the G8 looking like a political relic.

That's why Cameron has enthusiastically grasped the idea that alleviating poverty is not just about aid. He wants to harness public fury against tax dodgers at home, to fight for fairer international rules that force businesses to pay their way. Christian Aid estimates that companies dodge $160bn of corporation tax each year – enough, it says, to alleviate hunger for 75,000 children.

The prime minister speaks at the World Economic Forum in Davos, Switzerland.

The prime minister is also calling for more transparency about who owns what – to prevent secretive land-grabs in Africa and allow campaigners to fight for a fair share of natural resources, for example – and a renewed push to tear down trade barriers.

All of this goes with the grain of an economically liberal Tory party that is sceptical about the benefits of overseas aid (though Cameron is not abandoning his aid promises), but cherishes the idea of playing by the rules.

It helps avoid the risk that African governments feel excluded and talked down to by the dinosaurs in the G8: Cameron's message, instead, will be "we'll start by getting our house in order".

And, like Make Poverty History in the runup to the 2005 G8, it has been carefully choreographed to chime with a noisy grassroots campaign from a coalition of NGOs, which argues that there is enough food to feed the world, if only we make the global system work better.

It remains to be seen how much political muscle Britain's prepared to put behind the prime minister's rhetoric. But if Cameron achieved even one of his goals – forcing firms to pay their fair share of tax in each country in which they operate – Britain's G8 chairmanship would be something to celebrate.